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Also known as homogeneous dilation, homothety, homothecy, Homothetic transformation

thumb|upright=1|Homothety: Example with . corresponds to (no point is moved); an ; a thumb|upright=1|Example with . corresponds to a point reflection at point thumb|upright=1.2|Homothety of a pyramid In mathematics, a homothety (or homothecy, or homogeneous dilation) is a transformation of an affine space determined by a point called its center and a nonzero number called its ratio, which sends point to a point by the rule, \overrightarrow{SX'}=k\overrightarrow{SX} for a fixed number . Using position vectors: \mathbf x'=\mathbf s + k(\mathbf x -\mathbf s).